Correlation ≠ causation. Have you ever heard an admissions officer say it’s more important to have a 2400 than outstanding extracurriculars, essays, and teacher recommendations?
People with 2300+ SAT scores are also more likely to have other outstanding achievements and recommendations that would help them get into HYPMS. Honestly? I had next to no leadership positions, some very common ECs, and a couple disastrous interviews. That probably hurt my application more than scoring 680 on the writing section of the SAT (everything else was 750+, including subject tests).
And strangely enough, I still wouldn’t have done anything different. Failure is humbling, and college admissions can teach you a lot about what really matters.